Question

calcule a area de cada triangulo

Answer 1

Explicação passo-a-passo:

a)

$\sf p=\dfrac{16+18+20}{2}$

$\sf p=\dfrac{54}{2}$

$\sf p=27$

$\sf S=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$\sf S=\sqrt{27\cdot(27-16)\cdot(27-18)\cdot(27-20)}$

$\sf S=\sqrt{27\cdot11\cdot9\cdot7}$

$\sf S=\sqrt{18711}$

$\sf S=9\sqrt{231}~dm^2$

b)

$\sf S=\dfrac{b\cdot h}{2}$

$\sf S=\dfrac{12\cdot16}{2}$

$\sf S=\dfrac{192}{2}$

$\sf S=96~dm^2$

c)

Pelo Teorema de Pitágoras:

$\sf (b_1)^2+12^2=20^2$

$\sf (b_1)^2+144=400$

$\sf (b_1)^2=400-144$

$\sf (b_1)^2=256$

$\sf b_1=\sqrt{256}$

$\sf b_1=16~dm$

$\sf (b_2)^2+12^2=15^2$

$\sf (b_2)^2+144=225$

$\sf (b_2)^2=225-144$

$\sf (b_2)^2=81$

$\sf b_2=\sqrt{81}$

$\sf b_2=9~dm$

O outro lado desse triângulo mede:

$\sf b=b_1+b_2$

$\sf b=16+9$

$\sf b=25~dm$

Logo:

$\sf S=\dfrac{b\cdot h}{2}$

$\sf S=\dfrac{25\cdot12}{2}$

$\sf S=\dfrac{300}{2}$

$\sf S=150~dm^2$